Approximation of periodic functions by composite two-point Hermite polynomials

This paper deals with polynomial approximating a periodic functions by composite two-point Hermite polynomials. The final formulas of these polynomials, using the function values and its derivatives at a given point, are constructed. The relation of Taylor's polynomial and two-point polynomials with respect to representation of periodic function is specified. The estimation of proximity, expressed through the evaluation of the derivative of the corresponding order is given. A sufficient condition for the convergence of a sequence of two-point polynomials to a given periodic function is established. Examples are given in which periodic function is approximated by a sequence of two-point Hermite polynomials with data on an errors and its evaluation.